There are challenges in operating a three phase electric motor above base speed in a conventional Vector Control motor control system. These controllers operate in a 2-dimensional space called the DQ-plane where both the motor current and applied motor voltage are represented by two dimensional vectors. The two dimensional vectors are derived by transforming sinusoidal three phase current signals into the DQ plane via the Clark and Park transforms as known in the art per se. The DQ vectors are non-sinusoidal d.c. signals for a given motor speed, thus simplifying the control problem and minimizing the computational load requirements of the controller.
The conventional DQ controller utilizes two feedback control loops to determine DQ control voltages based on DQ currents. The DQ currents and voltages, however, have limits based on physical constraints.
More particularly, consider the ellipse 20 in FIG. 1A, which represents the permissible DQ motor currents for a base motor speed. The DQ current at any point in time will be somewhere within the ellipse 20. Likewise, the circle 30 in FIG. 1B represents the permissible DQ voltage, which is based on source voltage constraints and inverter capability. The DQ control voltage at any point in time will be somewhere within or at the edge of the circle 30.
Referring back to FIG. 1A, the permissible DQ currents, i.e., the size of the ellipse, will vary with motor speed and the applied DQ voltage. As the motor speed increases, the back electromotive force (emf) increases limiting the amount of current that can flow in the motor. Consequently, as the speed of the motor increases, the range of permissible DQ currents shrinks as exemplified by the size of the smaller ellipse 20′ shown in stippled lines.
Note that the limitation on applied voltage is not a function of motor operation and is determined only by the available source voltage. The radius of circle 30 in FIG. 1B thus remains essentially constant for a given source voltage.
It is generally desired to operate the electric motor under conditions of maximum power efficiency where I2R losses are minimized and the motor provides the most torque per ampere of current (MTPA). The MTPA curve, shown at ref. no. 24 in FIG. 1A, is typically derived empirically at a relatively low “base” motor speed so that large currents can be applied to the motor in order to flush out the nature of the curve 24.
Thus, for a given torque output, which is represented by one of curves 28 in FIG. 1A, the ideal DQ current to operate the motor is found on the MTPA curve 24. For example, if torque curve 28a represents 100 Nm output, the ideal DQ current is found at point 27, and the feedback control loop adjusts the DQ control voltages to achieve the DQ current represented by point 27. These operating conditions are relatively easy to achieve when the motor speed is low, however, as the motor speed increases the ideal voltage and current vectors are no longer physically possible. For example, at higher motor speeds where the achievable range of DQ currents is exemplified by the smaller ellipse 20′, the ideal MTPA point 27 for the 100 Nm output lies outside ellipse 20′. The DQ controller must thus use a less efficient operating point along the torque curve 28a, for example, at point 29.
Note that point 29 will not lie at the edge of the permissible range of DQ currents represented by ellipse 20′ because another problem exists at high speed when the applied DQ voltage reaches the limit circle 30. More particularly, the typical DQ vector controller may become unstable when the output voltage reaches this limit. Since points on the voltage circle 30 correspond with points on the current ellipse 20′, this leads to systems where the current must be kept inside the operating region without going all the way to the edge, else the control system may become unstable. By not allowing the DQ current and voltage to reach the physical limits, the system becomes less efficient. As a result, the system designer must trade efficiency for stability.
The stability problem arises from the manner in which the typical DQ current controller is constructed, where one feedback control loop regulates Vd based on changes in Id and another feedback control block regulates Vq based on changes in I4. The conventional construction assumes that, in order to cause an increase in Id, the system must first increase Vd, and that a similar relationship exists between Iq and Vq. The problem arises when the voltage limit circle is reached, and a change in Vd for example may force a change in Vd due to the limit circle, at which point the conventional DQ current controller essentially loses one degree of freedom. The instability is partially caused by the tension between the two feedback control loops when constrained by the circular voltage limit. The problem is exacerbated when the motor is run in the generator mode.